Beam support reactions worksheet with answers

Free printable Beam support reactions worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
M₀ = 10 kN·mABRA​ = ?2.5 m2.5 m

The simply supported beam has a pin at A and a roller at B. It carries only a counter-clockwise couple of 10 kN·m applied at 2.5 m from A. Find the vertical reaction RA, taking upward as positive.

L = 5 mM₀ = 10 kN·m (counter-clockwise) at 2.5 m
RA = kN
2.Easy
P = 70 kNABRA​ = ?RB​3.5 m1.5 m

The simply supported beam has a pin at A and a roller at B. Find the vertical support reaction RA.

L = 5 mP = 70 kN at 3.5 m
RA = kN
3.Medium
P1​ = 55 kNP2​ = 10 kNABRA​RB​ = ?3 m6 m1 m

The simply supported beam has a pin at A and a roller at B. Find the vertical support reaction RB.

L = 10 mP1 = 55 kN at 3 mP2 = 10 kN at 9 m
RB = kN
4.Medium
P1​ = 80 kNP2​ = 60 kNABCRA​ = ?3 m5 m2 m

The beam has a pin at A and a roller at B, 8 m from A, and overhangs B to the free end C. Find the vertical reaction RA, taking upward as positive.

AB = 8 mAC = 10 mP1 = 80 kN at 3 mP2 = 60 kN at 10 m
RA = kN
5.Hard
w = 10 kN/mP = 65 kNABCRB​ = ?3 m1 m0.5 m1.5 m

The beam has a pin at A and a roller at B, 4.5 m from A, and overhangs B to the free end C. It carries a point load P at 4 m from A and a uniformly distributed load w from 3 m to the free end at 6 m. Find the vertical reaction RB, taking upward as positive.

AB = 4.5 mAC = 6 mP = 65 kN at 4 mw = 10 kN/m from 3 to 6 m
RB = kN
6.Hard
w = 6 kN/mP = 45 kNADCMA​ = ?6 m2 m2 m

A compound beam is fixed to the wall at A, has an internal hinge at C (6 m from A) and rests on a roller at D (10 m from A). It carries a point load P at 8 m from A, a uniformly distributed load w on the whole part CD. Find the magnitude of the reaction moment MA at the wall.

AC = 6 mAD = 10 mP = 45 kN at 8 mw = 6 kN/m from 6 to 10 m
MA = kN·m

Answer key

  1. 1. RA = 2 kN
  2. 2. RA = 21 kN
  3. 3. RB = 25.5 kN
  4. 4. RA = 35 kN
  5. 5. RB = 87.78 kN
  6. 6. MA = 207 kN·m

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